Abstract

Since its introduction by Jennison in 1958, the closure-phase method for removing the effects of electrical path-length errors in radio astronomy and of atmospheric turbulence in optical astronomy has been based on the non-redundant-spacing triple interferometer. It is shown that through application of lucky imaging concepts it is possible to relax this condition, making closure-phase methods possible with redundantly spaced interferometer configurations and thereby widening their range of application. In particular, a quadruple-interferometer can, under lucky imaging conditions, be treated as though it were a triple interferometer. The slit-annulus aperture is investigated as a special case.

© 2008 Optical Society of America

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References

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  1. R. C. Jennison, “A phase sensitive interferometer technique for the measurement of the Fourier transforms of spatial brightness distributions of small angular extent,” Mon. Not. R. Astron. Soc. 118, 276-284 (1958).
  2. T. J. Cornwell, “The applications of closure phase to astronomical imaging,” Science 245, 263-269 (1989).
    [CrossRef] [PubMed]
  3. D. L. Fried, “Probability of getting a lucky short-exposure image through turbulence,” J. Opt. Soc. Am. 68, 1651-1658(1978).
    [CrossRef]
  4. J. E. Baldwin, P. J. Warner, and C. D. Mackay, “The point spread function in lucky imaging and variations in seeing on short timescales,” Astron. Astrophys. 480, 589-597 (2008).
    [CrossRef]
  5. G. W. Carhart and M. A. Vorontsov, “Synthetic imaging: nonadaptive anisoplanatic image correction in atmospheric turbulence,” Opt. Lett. 23, 745-747 (1998).
    [CrossRef]
  6. M. A. Vorontsov and G. W. Carhart, “Anisoplanatic imaging through turbulent media: image recovery by local information fusion from a set of short-exposure images,” J. Opt. Soc. Am. A 18, 1312-1324 (2001).
    [CrossRef]
  7. D. H. Rogstad, “A technique for measuring visibility phase with an optical interferometer in the presence of atmospheric seeing,” Appl. Opt. 7, 585-588 (1968).
    [CrossRef] [PubMed]
  8. W. T. Rhodes and J. W. Goodman, “Interferometric technique for recording and restoring images degraded by unknown aberrations,” J. Opt. Soc. Am. 63, 647-657 (1973).
    [CrossRef]
  9. See, e.g., W. T. Rhodes, “Image formation and the retransformation of coherence functions,” in The Art and Science of Holography: A Tribute to Emmett Leith and Yuri Denisyuk (SPIE Press, 2004), Chap. 7.
  10. C. A. Haniff and D. F. Buscher, “Diffraction-limited imaging with partially redundant masks. I. Infrared imaging of bright objects,” J. Opt. Soc. Am. A 9, 203-218 (1992).
    [CrossRef]
  11. J. E. Ward, W. T. Rhodes, and J. T. Sheridan, “Lucky imaging and aperture synthesis with low-redundancy apertures,” Appl. Opt. 48, (this issue).
    [PubMed]
  12. P. Tuthill, J. Lloyd, M. I. F. Martinache, J. Monnier, H. Woodruff, T. ten Brummelaar, N. Turner, and C. Townes, “Sparse-aperture adaptive optics,” Proc. SPIE 6272, 62723A(2006).
    [CrossRef]
  13. Labeyrie, S. G. Lipson, and P. Nisenson, An Introduction to Optical Stellar Interferometry, (Cambridge U. Press, 2006), Sect. 6.4.2.
  14. R. B. Holmes, S. Ma, A. Bhowmik, and C. Greninger, “Analysis and simulation of a synthetic-aperture technique for imaging through a turbulent medium,” J. Opt. Soc. Am. A 13, 351-364 (1996).
    [CrossRef]

2008 (1)

J. E. Baldwin, P. J. Warner, and C. D. Mackay, “The point spread function in lucky imaging and variations in seeing on short timescales,” Astron. Astrophys. 480, 589-597 (2008).
[CrossRef]

2006 (1)

P. Tuthill, J. Lloyd, M. I. F. Martinache, J. Monnier, H. Woodruff, T. ten Brummelaar, N. Turner, and C. Townes, “Sparse-aperture adaptive optics,” Proc. SPIE 6272, 62723A(2006).
[CrossRef]

2001 (1)

1998 (1)

1996 (1)

1992 (1)

1989 (1)

T. J. Cornwell, “The applications of closure phase to astronomical imaging,” Science 245, 263-269 (1989).
[CrossRef] [PubMed]

1978 (1)

1973 (1)

1968 (1)

1958 (1)

R. C. Jennison, “A phase sensitive interferometer technique for the measurement of the Fourier transforms of spatial brightness distributions of small angular extent,” Mon. Not. R. Astron. Soc. 118, 276-284 (1958).

Baldwin, J. E.

J. E. Baldwin, P. J. Warner, and C. D. Mackay, “The point spread function in lucky imaging and variations in seeing on short timescales,” Astron. Astrophys. 480, 589-597 (2008).
[CrossRef]

Bhowmik, A.

Buscher, D. F.

Carhart, G. W.

Cornwell, T. J.

T. J. Cornwell, “The applications of closure phase to astronomical imaging,” Science 245, 263-269 (1989).
[CrossRef] [PubMed]

Fried, D. L.

Goodman, J. W.

Greninger, C.

Haniff, C. A.

Holmes, R. B.

Jennison, R. C.

R. C. Jennison, “A phase sensitive interferometer technique for the measurement of the Fourier transforms of spatial brightness distributions of small angular extent,” Mon. Not. R. Astron. Soc. 118, 276-284 (1958).

Labeyrie,

Labeyrie, S. G. Lipson, and P. Nisenson, An Introduction to Optical Stellar Interferometry, (Cambridge U. Press, 2006), Sect. 6.4.2.

Lipson, S. G.

Labeyrie, S. G. Lipson, and P. Nisenson, An Introduction to Optical Stellar Interferometry, (Cambridge U. Press, 2006), Sect. 6.4.2.

Lloyd, J.

P. Tuthill, J. Lloyd, M. I. F. Martinache, J. Monnier, H. Woodruff, T. ten Brummelaar, N. Turner, and C. Townes, “Sparse-aperture adaptive optics,” Proc. SPIE 6272, 62723A(2006).
[CrossRef]

Ma, S.

Mackay, C. D.

J. E. Baldwin, P. J. Warner, and C. D. Mackay, “The point spread function in lucky imaging and variations in seeing on short timescales,” Astron. Astrophys. 480, 589-597 (2008).
[CrossRef]

Martinache, M. I. F.

P. Tuthill, J. Lloyd, M. I. F. Martinache, J. Monnier, H. Woodruff, T. ten Brummelaar, N. Turner, and C. Townes, “Sparse-aperture adaptive optics,” Proc. SPIE 6272, 62723A(2006).
[CrossRef]

Monnier, J.

P. Tuthill, J. Lloyd, M. I. F. Martinache, J. Monnier, H. Woodruff, T. ten Brummelaar, N. Turner, and C. Townes, “Sparse-aperture adaptive optics,” Proc. SPIE 6272, 62723A(2006).
[CrossRef]

Nisenson, P.

Labeyrie, S. G. Lipson, and P. Nisenson, An Introduction to Optical Stellar Interferometry, (Cambridge U. Press, 2006), Sect. 6.4.2.

Rhodes, W. T.

W. T. Rhodes and J. W. Goodman, “Interferometric technique for recording and restoring images degraded by unknown aberrations,” J. Opt. Soc. Am. 63, 647-657 (1973).
[CrossRef]

See, e.g., W. T. Rhodes, “Image formation and the retransformation of coherence functions,” in The Art and Science of Holography: A Tribute to Emmett Leith and Yuri Denisyuk (SPIE Press, 2004), Chap. 7.

J. E. Ward, W. T. Rhodes, and J. T. Sheridan, “Lucky imaging and aperture synthesis with low-redundancy apertures,” Appl. Opt. 48, (this issue).
[PubMed]

Rogstad, D. H.

Sheridan, J. T.

J. E. Ward, W. T. Rhodes, and J. T. Sheridan, “Lucky imaging and aperture synthesis with low-redundancy apertures,” Appl. Opt. 48, (this issue).
[PubMed]

ten Brummelaar, T.

P. Tuthill, J. Lloyd, M. I. F. Martinache, J. Monnier, H. Woodruff, T. ten Brummelaar, N. Turner, and C. Townes, “Sparse-aperture adaptive optics,” Proc. SPIE 6272, 62723A(2006).
[CrossRef]

Townes, C.

P. Tuthill, J. Lloyd, M. I. F. Martinache, J. Monnier, H. Woodruff, T. ten Brummelaar, N. Turner, and C. Townes, “Sparse-aperture adaptive optics,” Proc. SPIE 6272, 62723A(2006).
[CrossRef]

Turner, N.

P. Tuthill, J. Lloyd, M. I. F. Martinache, J. Monnier, H. Woodruff, T. ten Brummelaar, N. Turner, and C. Townes, “Sparse-aperture adaptive optics,” Proc. SPIE 6272, 62723A(2006).
[CrossRef]

Tuthill, P.

P. Tuthill, J. Lloyd, M. I. F. Martinache, J. Monnier, H. Woodruff, T. ten Brummelaar, N. Turner, and C. Townes, “Sparse-aperture adaptive optics,” Proc. SPIE 6272, 62723A(2006).
[CrossRef]

Vorontsov, M. A.

Ward, J. E.

J. E. Ward, W. T. Rhodes, and J. T. Sheridan, “Lucky imaging and aperture synthesis with low-redundancy apertures,” Appl. Opt. 48, (this issue).
[PubMed]

Warner, P. J.

J. E. Baldwin, P. J. Warner, and C. D. Mackay, “The point spread function in lucky imaging and variations in seeing on short timescales,” Astron. Astrophys. 480, 589-597 (2008).
[CrossRef]

Woodruff, H.

P. Tuthill, J. Lloyd, M. I. F. Martinache, J. Monnier, H. Woodruff, T. ten Brummelaar, N. Turner, and C. Townes, “Sparse-aperture adaptive optics,” Proc. SPIE 6272, 62723A(2006).
[CrossRef]

Appl. Opt. (2)

D. H. Rogstad, “A technique for measuring visibility phase with an optical interferometer in the presence of atmospheric seeing,” Appl. Opt. 7, 585-588 (1968).
[CrossRef] [PubMed]

J. E. Ward, W. T. Rhodes, and J. T. Sheridan, “Lucky imaging and aperture synthesis with low-redundancy apertures,” Appl. Opt. 48, (this issue).
[PubMed]

Astron. Astrophys. (1)

J. E. Baldwin, P. J. Warner, and C. D. Mackay, “The point spread function in lucky imaging and variations in seeing on short timescales,” Astron. Astrophys. 480, 589-597 (2008).
[CrossRef]

J. Opt. Soc. Am. (2)

J. Opt. Soc. Am. A (3)

Mon. Not. R. Astron. Soc. (1)

R. C. Jennison, “A phase sensitive interferometer technique for the measurement of the Fourier transforms of spatial brightness distributions of small angular extent,” Mon. Not. R. Astron. Soc. 118, 276-284 (1958).

Opt. Lett. (1)

Proc. SPIE (1)

P. Tuthill, J. Lloyd, M. I. F. Martinache, J. Monnier, H. Woodruff, T. ten Brummelaar, N. Turner, and C. Townes, “Sparse-aperture adaptive optics,” Proc. SPIE 6272, 62723A(2006).
[CrossRef]

Science (1)

T. J. Cornwell, “The applications of closure phase to astronomical imaging,” Science 245, 263-269 (1989).
[CrossRef] [PubMed]

Other (2)

See, e.g., W. T. Rhodes, “Image formation and the retransformation of coherence functions,” in The Art and Science of Holography: A Tribute to Emmett Leith and Yuri Denisyuk (SPIE Press, 2004), Chap. 7.

Labeyrie, S. G. Lipson, and P. Nisenson, An Introduction to Optical Stellar Interferometry, (Cambridge U. Press, 2006), Sect. 6.4.2.

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Figures (4)

Fig. 1
Fig. 1

Single-lens imaging system for planar, spatially incoherent, quasi-monochromatic objects. The system is equipped with a pinhole mask in the pupil plane. A piece of randomly rippled shower glass can be added to simulate the effect of short-exposure imaging through nearby atmospheric turbulence.

Fig. 2
Fig. 2

Pinhole masks (a) and (c), with associated optical transfer function diagrams (b) and (d). The pairs of numbers in (b) and (d) indicate the pinholes associated with specific spatial frequencies.

Fig. 3
Fig. 3

Slit-annulus aperture and associated image spatial frequency diagram. The two pairs of local regions of the aperture labeled 1, 2, and 3, 4—think of them in analogy with pinholes—contribute to the image at spatial frequency ρ 12 = ρ 34 and its negative-frequency counterpart - ρ 12 = - ρ 34 with a redundancy of 2. Lucky imaging conditions are designated by the L in parentheses, which appears along with the redundancy number.

Fig. 4
Fig. 4

Cross section of the OTF associated with a thin annular aperture. The inner radius equals 95% of outer radius for this example. The relatively flat mid-region corresponds to low- redundancy spatial frequencies and is suitable for lucky phase- closure calculations.

Equations (8)

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θ ( ρ 12 ) = ψ ( ρ 12 ) + ϕ 2 - ϕ 1 ,
θ ( ρ 23 ) = ψ ( ρ 23 ) + ϕ 3 - ϕ 2 ,
θ ( ρ 13 ) = ψ ( ρ 13 ) + ϕ 3 - ϕ 1 .
Θ ( ρ 12 , ρ 23 , ρ 13 ) = θ ( ρ 12 ) + θ ( ρ 23 ) - θ ( ρ 13 ) = ψ ( ρ 12 ) + ψ ( ρ 23 ) - ψ ( ρ 13 ) .
Θ ( ρ 12 , ρ 24 , ρ 14 ) = θ ( ρ 12 ) + θ ( ρ 24 ) - θ ( ρ 14 ) = ψ ( ρ 12 ) + ψ ( ρ 24 ) - ψ ( ρ 14 ) .
Θ ( ρ 12 , ρ 23 , ρ 13 ) = θ ( ρ 12 ) + θ ( ρ 23 ) - θ ( ρ 13 ) = ψ ( ρ 12 ) + ψ ( ρ 23 ) - ψ ( ρ 13 ) + ( Δ ϕ 43 - Δ ϕ 32 ) / 2 ,
( ρ 23 ) = 2 4 1 + cos ( Δ ϕ 43 - Δ ϕ 32 ) × exp ( j Δ ϕ 43 + Δ ϕ 3 2 2 ) .
Θ ( ρ 12 , ρ 32 , ρ 41 ) = 2 θ ( ρ 12 ) - θ ( ρ 32 ) + θ ( ρ 41 ) = 2 [ ψ ( ρ 12 ) + ϕ 2 - ϕ 1 ] - [ ψ ( ρ 32 ) + ϕ 2 - ϕ 3 ] + [ ψ ( ρ 41 ) + ϕ 1 - ϕ 4 ] = 2 ψ ( ρ 12 ) - ψ ( ρ 32 ) + ψ ( ρ 41 ) ,

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